Compactness of $\omega^\lambda$ for $\lambda$ singular
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We characterize the compactness properties of the product of \lambda\ copies of the space \omega\ with the discrete topology, dealing in particular with the case \lambda\ singular, using regular and uniform ultrafilters, infinitary languages and nonstandard elements. We also deal with products of uncountable regular cardinals with the order topology.
Comment: Treats the case \lambda\ singular only hinted in arXiv:1302.4763; v2 some very minor improvements and corrections
finally compact topological space, weakly compact cardinal, ultrafilter convergence, λ)-regular ultrafilter, Primary 54B10, 54D20, 03C75, Secondary 03C20, 03E05, 54A20, infinitary language, Mathematics - Logic, Settore MAT/01 - LOGICA MATEMATICA, Powers of omega; finally compact topological space; infinitary language; ultrafilter convergence, limit point; uniform, (λ, λ)-regular ultrafilter; nonstandard element; weakly compact cardinal, Powers of omega, (λ, uniform, limit point, nonstandard element, Mathematics - General Topology
finally compact topological space, weakly compact cardinal, ultrafilter convergence, λ)-regular ultrafilter, Primary 54B10, 54D20, 03C75, Secondary 03C20, 03E05, 54A20, infinitary language, Mathematics - Logic, Settore MAT/01 - LOGICA MATEMATICA, Powers of omega; finally compact topological space; infinitary language; ultrafilter convergence, limit point; uniform, (λ, λ)-regular ultrafilter; nonstandard element; weakly compact cardinal, Powers of omega, (λ, uniform, limit point, nonstandard element, Mathematics - General Topology
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